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Warm-Up: January 30, 2012

Warm-Up: January 30, 2012. Where do we encounter waves? Write down all the examples of waves that you can think of. Vibrations and Waves. Chapter 14. Periodic Motion. A periodic motion repeats in a regular cycle. Examples include: Pendulums (such as on a grandfather clock)

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Warm-Up: January 30, 2012

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  1. Warm-Up: January 30, 2012 • Where do we encounter waves? Write down all the examples of waves that you can think of.

  2. Vibrations and Waves Chapter 14

  3. Periodic Motion • A periodic motion repeats in a regular cycle. • Examples include: • Pendulums (such as on a grandfather clock) • A mass at the end of a spring • Vibrating guitar string • The period is the amount of time for one complete cycle. • The amplitude is the maximum amount that the object moves from its initial, equilibrium position

  4. Periodic Motion Graph x

  5. Springs • When you stretch or compress a spring, the spring exerts a force to return it to its equilibrium position. • The amount of force is given by Hooke’s Law • where k is the spring constant (a property of the individual spring) • and x is the distance the spring is from its equilibrium position

  6. Example 1 • How much force is needed to stretch a spring 25 cm if the spring constant is 105 N/m?

  7. You-Try #1 • How much force is needed to compress a spring 12 cm if the spring constant is 84 N/m?

  8. Energy of Springs • Stretching or compressing a spring also generates elastic potential energy • This is a different type of potential energy than the gravitational potential energy we’ve discussed

  9. Example 2 • A spring has a spring constant of 256 N/m. How far must it be stretched to give it an elastic potential energy of 48 J?

  10. You-Try #2 • A spring with a spring constant of 144 N/m is compressed by a distance of 16.5 cm. How much elastic potential energy is stored in the spring?

  11. Resonance • Resonance occurs when small forces are applied at regular intervals to an object in periodic motion causing the amplitude to increase. • Examples include: • Pushing someone on a swing • Jumping on a diving board • Wind on the Tacoma Narrows Bridge

  12. Warm-Up: January 31, 2012 • A spring has a spring constant of 125 N/m. It is attached to the ceiling and a block is attached to the bottom. The spring is stretched 20.0 cm. • Draw a free body diagram of the block. • What force does the spring exert on the mass? • What is the weight of the block? • What is the elastic potential energy stored in the spring?

  13. Waves • A wave is a disturbance that carries energy through matter or space • A wave usually does NOT transfer mass, only energy • A wave pulse is a single bump or disturbance. Most waves are a series of wave pulses. • Two main types of waves: • Mechanical waves – travel through matter • Electromagnetic waves – do not require matter, can travel through a vacuum

  14. Mechanical Waves • Examples include: • Water waves • Sound waves • Waves on a rope • Waves on a spring • Mechanical waves require a medium (matter) through which they propagate (travel). • Three main categories: • Transverse Waves • Longitudinal Waves • Surface Waves

  15. Transverse Waves • A transverse wave is one that vibrates perpendicular to the direction of the wave’s motion • A wave on a rope is an example of a transverse wave • Simulation

  16. Parts of a Transverse Wave • Crest – The highest point • Trough – The lowest point • Amplitude – The maximum displacement of of the wave • The higher the amplitude, the greater the amount of energy transferred. • Wavelength – The distance between crests (or the distance between troughs)

  17. Think, Pair, Share • Identify which point(s) correspond with each of the following: crest, trough, amplitude, wavelength

  18. Longitudinal Waves • A longitudinal wave is one whose disturbances are in the same direction as (parallel to) the direction of the wave’s motion • Sound waves are longitudinal • Waves from a compressed spring are longitudinal

  19. Parts of a Longitudinal Wave • Compression – A dense part of a longitudinal wave • Rarefaction – A low density part of a longitudinal wave • Wavelength – The distance between compressions (or the distance between rarefactions)

  20. Warm-Up: February 1, 2012 • A man with a mass of 75 kg hangs from a spring that is attached to the ceiling, causing it to stretch 83 cm (after the oscillations stop). What is the spring constant of the spring?

  21. Surface Waves • Surface waves are waves with characteristics of both transverse and longitudinal waves. • Ocean waves are a prime example of surface waves. • The paths of individual particles are circular.

  22. Measuring Waves • The following are all used to measure and/or describe waves: • Wave Speed • Amplitude • Period • Frequency • Wavelength

  23. Wave Speed • Wave Speed – The distance a wave travels per unit time • Represented by a lower case v • Measured in meters per second, m/s • Depends on the medium through which the wave is travelling

  24. Amplitude • Amplitude – The maximum displacement of a wave from its at-rest position • Represented by a capital A • Measured in meters, m • Depends on how the wave was generated • Does not depend on the wave speed or the medium • More work must be done to generate larger amplitude waves. • Waves with larger amplitudes transfer more energy

  25. Period • Period - the amount of time for one complete cycle/oscillation • Represented by a capital T • Measured in seconds • Depends only on the wave source • Does not depend on the wave speed • Does not depend on the medium

  26. Frequency • Frequency – The amount of cycles/oscillations per second • Represented by a lower case f • Measured in Hertz, Hz • Depends only on the wave source • Does not depend on the wave speed • Does not depend on the medium

  27. Wavelength • Wavelength – Length of a cycle (distance between similar points) • Distance between crests (or troughs) of a transverse wave • Distance between compressions (or rarefactions) of a longitudinal wave • Represented by Greek letter lambda, λ • Measured in meters

  28. Example 3 • Sound waves travel approximately 340 m/s in air. What is the wavelength of a sound wave that has a frequency of 170 Hz? 2.0 m

  29. You-Try #3 • Sound has a speed of 3100 m/s in copper. What is the wavelength of the wave from Example 3 after it crosses into a copper medium? 18 m

  30. Wave Reflection • What happens when a wave reaches the end of its medium? • When the incident wave reaches the end of its medium,some or all of the energy is reflected back as a reflected wave. • Some reflected waves are inverted, such as waves on a rope with a fixed end (as in the simulation)

  31. Warm-Up: February 6, 2012 • A sound wave produced by a clock chime is heard 515 m away 1.50 s later. • What is the speed of the clock’s chime in air? • If the sound wave has a frequency of 436 Hz, what is the period of the wave? • What is the wave’s wavelength?

  32. Homework Questions?

  33. Superposition • The principle of superposition states that the amplitude of passing wave pulses is additive. • If pulses are on opposite sides, one amplitude is negative (adding a negative  subtracting) • The result of superposition is called interference.

  34. Superposition Examples

  35. Standing Waves • Interference can cause standing waves, which appear to not propagate. • Example: Rope moves up and down, but no wave pulses move to either side. • The nodes are points that do not move. • The antinodes are the points that move the most. • Simulation: Amplitude=20, Frequency=30, Damping=0, Tension=high-1

  36. Standing Waves in Music • Stringed instruments depend on standing waves to make music. • These standing waves are called harmonics.

  37. Warm-Up: February 7, 2012 • A wave has a frequency of 225 Hz. What is its period? • The wave changes medium from air to water. What happens to the period? (increase, remain constant, or decrease)

  38. Homework Questions?

  39. Waves in Two Dimensions • Often represented by a wave front, a line that represents a wave crest. • Waves move perpendicular to the wave front, often represented by a ray.

  40. Reflection of 2-D Waves • The law of reflection states that the angle of incidence equals the angle of reflection

  41. Assignment • Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71, 72, 76, 79, 81

  42. Classwork • Read Conceptual Physics chapter 25 (pages 372-386) • Answer review questions #1-20 on p. 387-388

  43. Warm-Up: February 13, 2012 • List the five characteristics that are used to measure/describe waves. • Which of the above depend on the medium through which the wave is travelling?

  44. Waves Worksheet Answers • energy • matter • transverse • longitudinal • surface • transverse • energy, formation • speed, wavelength

  45. Waves Worksheet Answers • The speed of a wave is equal to its wavelength divided by its period. • If the frequency of a wave decreases while wave speed remains constant, the wavelength increases. • The wavelength of a longitudinal wave is the distance between compressions (or rarefactions). The wavelength of a transverse wave is the distance between crests (or troughs).

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